Proof of Divisibility

[kiddopop]

Decide whether the following statement is true or false. If it is true, show that it is true, marking your argument as general as possible. If it is false, desprove it by finding a counterexample.

For all integers a and b, if a^2 divides b, the a^3 divides b^2.

 

[daon]

Think about this: If a^2 | b, then a^4 | b^2.

 

[kiddopop]

So you're saying the statement is false?

 

[mmm4444bot]

I'll try a different approach, to get you to think.

If a^2 divides b, then the result of that division must be a Natural number n.

b/a^2 = n

Clearly, b = a^2 * n

If that's b, then what is b^2/a^3 ?